If only the strict part of social preference is required to be transitive then Independence of Irrelevant Alternatives implies that there is a coalition containing all but one individual that cannot force x to be socially ranked above y for at least half of the pairs of alternatives (x,y)

We investigate the implications of relaxing Arrow's independence of irrelevant alternatives axiom while retaining transitivity and the Pareto condition. Even a small relaxation opens a floodgate of possibilities for nondictatorial and efficient social choice